# TrafficFlowGAN: Physics-informed Flow based Generative Adversarial Network for Uncertainty Quantification

arXiv: https://arxiv.org/abs/2206.09319 · HTML: https://mlsanity.com/paper/2206.09319/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 19 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/1811.04026/) (2018)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models](https://mlsanity.com/paper/2108.12956/) (2021)
- [AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows](https://mlsanity.com/paper/1905.12892/) (2019)
- [PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics](https://mlsanity.com/paper/2106.02993/) (2021)
- [Principled Interpolation in Normalizing Flows](https://mlsanity.com/paper/2010.12059/) (2020)

## Built on by (most cited first, 11 of 11)

- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [DriveGenVLM: Real-world Video Generation for Vision Language Model based Autonomous Driving](https://mlsanity.com/paper/2408.16647/) (2024)
- [Enhancing Multi-Hop Knowledge Graph Reasoning through Reward Shaping Techniques](https://mlsanity.com/paper/2403.05801/) (2024)
- [GenDDS: Generating Diverse Driving Video Scenarios with Prompt-to-Video Generative Model](https://mlsanity.com/paper/2408.15868/) (2024)
- [A Gentle Introduction and Tutorial on Deep Generative Models in Transportation Research](https://mlsanity.com/paper/2410.07066/) (2024)
- [Knowledge-data fusion oriented traffic state estimation: A stochastic physics-informed deep learning approach](https://mlsanity.com/paper/2409.00644/) (2024)
- [A Survey on the Application of Generative Adversarial Networks in Cybersecurity: Prospective, Direction and Open Research Scopes](https://mlsanity.com/paper/2407.08839/) (2024)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [PMA-Diffusion: A Physics-guided Mask-Aware Diffusion Framework for TSE from Sparse Observations](https://mlsanity.com/paper/2512.06183/) (2025)
- [Sim-MSTNet: sim2real based Multi-task SpatioTemporal Network Traffic Forecasting](https://mlsanity.com/paper/2601.21384/) (2026)

## Abstract (arXiv)

This paper proposes the TrafficFlowGAN, a physics-informed flow based generative adversarial network (GAN), for uncertainty quantification (UQ) of dynamical systems. TrafficFlowGAN adopts a normalizing flow model as the generator to explicitly estimate the data likelihood. This flow model is trained to maximize the data likelihood and to generate synthetic data that can fool a convolutional discriminator. We further regularize this training process using prior physics information, so-called physics-informed deep learning (PIDL). To the best of our knowledge, we are the first to propose an integration of flow, GAN and PIDL for the UQ problems. We take the traffic state estimation (TSE), which aims to estimate the traffic variables (e.g. traffic density and velocity) using partially observed data, as an example to demonstrate the performance of our proposed model. We conduct numerical experiments where the proposed model is applied to learn the solutions of stochastic differential equations. The results demonstrate the robustness and accuracy of the proposed model, together with the ability to learn a machine learning surrogate model. We also test it on a real-world dataset, the Next Generation SIMulation (NGSIM), to show that the proposed TrafficFlowGAN can outperform the baselines, including the pure flow model, the physics-informed flow model, and the flow based GAN model.